The study aims at showing that the general term or sequence of the Riemann zeta function is a polynomial time algorithm or Turing machine M which is used to resolve the computer science theory: P = NP? ξ(s)depends on the set of analytic zeros s = σ+it as raw materials while s depends on t, where t and σ are real numbers. The work shows that in polynomial time s(|t|) and for all strings of integer values n ≥ 1, M is closed and bounded of real values: [0, 1]. The algorithm M satisfies Cook’s theorem which is an NP-Complete problem. Hence, M is NP-Hard and hence NP-Complete and thus resolves the P = NP? problem at polynomial time s(|t|).